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Sahithyan's S1
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Dimensions & Units
Electrical Fundamentals
Basics
Introduction
Generation of Electricity
Common Terms
Circuit elements
Resistors
Capacitors
Inductors
Kirchhoff Laws
Waves
AC Theory
Phasor Representation
Impedance & Admittance
Power and Power factor
Power systems
Lab Apparatus
3-Phased System
Electrical Installation
Introduction
Fuses
Circuit Breaker
MCB
ELCB
RCD
RCCB
Earthing
Household Wiring
Installation Tests
Electric Shock
Fluid Mechanics
Statics
Introduction
Properties of Fluids
Hydrostatic Pressure
Pressure Measurements
Hydrostatic Thrust
Buoyancy
Stability of a Body
Relative Equilibrium
Forced Vortex Motion
Dynamics
Introduction
Classification of Fluid Flow
Conservation Laws
Derivations
Losses
Machinery
Introduction
Pumps
Centrifugal Pumps
Turbines
Mathematics
Vectors
Introduction
Section Formula
Straight Lines
Planes
Skew Lines
Matrices
Introduction
Matrix Multiplication
Transpose
More Types of Matrices
Determinant
Adjoint
Inverse
Elementary Transformations
Echelon Form
System of Linear Equations
Rank
Solutions of Homogenous Systems
Solution of Non-homogenous Systems
Eigenvalues & Eigenvectors
Orthogonal
Orthonormal
Trace
Diagonalization
Cayley-Hamilton Theorem
Matrix Norms
Complex Analysis
Introduction
Roots of Unity
Complex Functions
Limits
Continuity
Differentiability
Analytic Functions
Cauchy-Riemann Equations
Entire Functions
Real Analysis
Introduction
Set theory
Set of Numbers
Continued Fraction Expansion
Field Axioms
Completeness Axiom
Order Axioms
Relations
Functions
Composition
Countability
Limits
Known Limits
Continuity
Continuity Theorems
Differentiability
Extremums
Other Theorems
Higher Order Derivatives
Taylor's Theorem
Sequence
Cauchy Sequence
Subsequence
Series
Convergence Tests
Known Series
Alternating Series
Strategy for Series
Power Series
Taylor Series
Sequence of Functions
Uniformly Cauchy
Series of Functions
Riemann Zeta Function
ODE
Introduction
Solving First Order ODE
Higher Order ODE
Solving Second Order ODE
Wronskian
Variation of parameters
Riemann Integration
Introduction
Partition
Riemann Sum
Refinements
Upper & Lower integral
Riemann Integrable
Cauchy Criterion
Theorems on Integrability
Properties of Integrals
Sequential Characterization of Integrability
IVT for Integrals
Generlized IVT
Converging Functions
Fundamental Theorem of Calculus
Improper Riemann Integrals
Gamma function
Beta function
Mechanics
Statics
Introduction
Parallel Axis Theorem
Perpendicular Axis Theorem
Transformation Law
Principal Axes
Beams
Structural Elements
Trusses
Analysis of Trusses
Beam Analogy
Types of Trusses
Dynamics
Introduction
2D kinematics of a rigid body
Mechanisms
Four-bar Mechanism
Gears
Velocity & Acceleration Diagram
Inversions of a mechanism
Kinetic Analysis
Programming Fundamentals
A book
Introduction
Python Programming
Interning
Built-in Functions
String formatting
OOP
Practice Resources
B book
Introduction
Number Systems
Data Representation
Integers
Floating-point Numbers
Strings
Data Types
Algorithms
Software Engineering
C book
Introduction
Computer Hardware
CPU
CPU Instructions
CPU Support Chips
Von Neumann Architecture
Computer Memory
Secondary Storage
Magnetic Storage
Computer Software
Operating System
Embedded System
Arduino
Properties of Materials
Basics
Introduction
Structure of Atoms
Metals
Ceramics
Polymers
Composites
Crystal Structure
Space Lattice
Summary of the 4
Miller Indices
Allotropy
Defects in Crystals
Functional Materials
Selection of Materials
Mechanical Properties
Introduction
Ductility
Fracture
Elasticity
Poisson's ratio
Tensile Test
Stress Strain Plot
Flexural Test
Ductile-Brittle Transition
Work Hardening
Toughness
Charpy Impact Test
Hardness
Indentation Test
Electrical Properties
Introduction
Energy Band Theory
Semiconductivity
Dielectric behavior
Piezoelectricity
Conductive Polymers
Nanotechnology
Introduction
Graphene
Carbon Nanotubes
Degradation
Introduction
Degradation of Metals
Forms of Corrosion
Prevention of Corrosion
Degradation of Polymers
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Sahithyan's S1 — Mathematics
Known Limits
Well-known limits
Existing limits
Limits that DNE
Indeterminate forms